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Sep 20, 2013
09/13

by
Philip D. Mannheim

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We discuss our understanding of the equivalence principle in both classical mechanics and quantum mechanics. We show that not only does the equivalence principle hold for the trajectories of quantum particles in a background gravitational field, but also that it is only because of this that the equivalence principle is even to be expected to hold for classical particles at all.

Source: http://arxiv.org/abs/gr-qc/9810087v2

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Jun 29, 2018
06/18

by
Philip D. Mannheim

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In 2013 the Nobel Prize in Physics was awarded to Francois Englert and Peter Higgs for their work in 1964 along with the late Robert Brout on the mass generation mechanism (the Higgs mechanism) in local gauge theories. This mechanism requires the existence of a massive scalar particle, the Higgs boson, and in 2012 the Higgs boson was finally discovered at the Large Hadron Collider after being sought for almost half a century. In this article we review the work that led to the discovery of the...

Topics: High Energy Physics - Theory, High Energy Physics - Phenomenology

Source: http://arxiv.org/abs/1610.08907

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Jun 29, 2018
06/18

by
Philip D. Mannheim

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We revisit Weyl's metrication (geometrization) of electromagnetism. We show that by making Weyl's proposed geometric connection be pure imaginary, not only are we able to metricate electromagnetism, an underlying local conformal invariance makes the geometry be strictly Riemannian and prevents observational gravity from being complex. Via torsion we achieve an analogous metrication for axial-vector fields. We generalize our procedure to Yang-Mills theories, and achieve a metrication of all the...

Topics: High Energy Physics - Theory, General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1603.08405

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Jun 30, 2018
06/18

by
Philip D. Mannheim

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In applications of Einstein gravity one replaces the quantum-mechanical energy-momentum tensor of sources such as the degenerate electrons in a white dwarf or the black-body photons in the microwave background by c-number matrix elements. And not only that, one ignores the zero-point fluctuations in these sources by only retaining the normal-ordered parts of those matrix elements. There is no apparent justification for this procedure, and we show that it is precisely this procedure that leads...

Topics: High Energy Physics - Theory, General Relativity and Quantum Cosmology, High Energy Physics -...

Source: http://arxiv.org/abs/1703.09286

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Sep 22, 2013
09/13

by
Philip D. Mannheim

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The recent discovery of cosmic repulsion represents a major challenge to standard gravity, adding an apparent missing energy problem to its still not yet adequately resolved missing mass one, while simultaneously requiring the current universe to be a very special, fine-tuned one. We suggest that the resolution of these difficulties lies not in the existence of more and more exotic gravitational sources, but rather in the lack of reliability of the extrapolation of standard gravity from its...

Source: http://arxiv.org/abs/astro-ph/9807122v1

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Sep 17, 2013
09/13

by
Philip D. Mannheim

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While Hermiticity of a time-independent Hamiltonian leads to unitary time evolution, in and of itself, the requirement of Hermiticity is only sufficient for unitary time evolution. In this paper we provide conditions that are both necessary and sufficient. We show that $PT$ symmetry of a time-independent Hamiltonian, or equivalently, reality of the secular equation that determines its eigenvalues, is both necessary and sufficient for unitary time evolution. For any $PT$-symmetric Hamiltonian...

Source: http://arxiv.org/abs/0912.2635v3

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Sep 22, 2013
09/13

by
Philip D. Mannheim; Demosthenes Kazanas

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In the standard treatment of the Einstein gravitational theory the energy-momentum tensor has always been taken to be composed of perfect fluid aggregates of kinematic Newtonian point test particles with fundamental mechanical masses. Moreover, this standard prescription was not revised after the discovery of the mass-generating Higgs mechanism which is known to be present in the elementary particle physics of these self-same sources and which is also required in the conformal invariant...

Source: http://arxiv.org/abs/gr-qc/9409050v1

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Jun 28, 2018
06/18

by
Philip D. Mannheim

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We extend the $CPT$ theorem to quantum field theories with non-Hermitian Hamiltonians and unstable states. Our derivation is a quite minimal one as it requires only the time independent evolution of scalar products, invariance under complex Lorentz transformations, and a non-standard but nonetheless perfectly legitimate interpretation of charge conjugation as an anti-linear operator. The first of these requirements does not force the Hamiltonian to be Hermitian. Rather, it forces its...

Topics: Quantum Physics, Mathematical Physics, Mathematics, High Energy Physics - Phenomenology, High...

Source: http://arxiv.org/abs/1512.03736

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Jun 30, 2018
06/18

by
Philip D. Mannheim; J. J. Poveromo

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In this paper we show that in the presence of torsion and a metric with an antisymmetric part one can construct a gravitational analog of Faraday's law of electromagnetism.

Topic: General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1406.1470

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Sep 22, 2013
09/13

by
Philip D. Mannheim; Jan Kmetko

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We continue our study of the astrophysical implications of the linear potential $V(r)=-\beta c^2/r+\gamma c^2 r/2$ associated with fundamental gravitational sources in the conformal invariant fourth order theory of gravity which has recently been advanced by Mannheim and Kazanas as a candidate alternative to the standard second order Einstein theory. We provide fitting to the rotation curves of an extensive and diverse set of 11 spiral galaxies whose data are regarded as being particularly...

Source: http://arxiv.org/abs/astro-ph/9602094v1

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Sep 18, 2013
09/13

by
PHILIP D. MANNHEIM

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In a previous paper we presented a typical set of galactic rotation curves associated with the linear gravitational potential of the conformal invariant fourth order theory of gravity which has recently been advanced by Mannheim and Kazanas as a candidate alternative to the standard second order Newton-Einstein theory. Reasonable agreement with data was obtained for four representative galaxies without the need for any non-luminous or dark matter. In this paper we present the associated...

Source: http://arxiv.org/abs/astro-ph/9504022v1

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Sep 22, 2013
09/13

by
Philip D. Mannheim

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We review some recent developments in the conformal gravity theory that has been advanced as a candidate alternative to standard Einstein gravity. As a quantum theory the conformal theory is both renormalizable and unitary, with unitarity being obtained because the theory is a $PT$ symmetric rather than a Hermitian theory. We show that in the theory there can be no a priori classical curvature, with all curvature having to result from quantization. In the conformal theory gravity requires no...

Source: http://arxiv.org/abs/1101.2186v2

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Jun 29, 2018
06/18

by
Philip D. Mannheim

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In a quantum electrodynamics theory that is realized by critical scaling and anomalous dimensions, the action is not chiral invariant and there are no dynamical Goldstone or Higgs boson bound states. In the mean-field approximation to a chiral invariant four-fermion theory the associated mean-field sector action is not chiral invariant either and it also possesses no dynamical bound states, with Goldstone and Higgs bosons instead being generated by an accompanying four-fermion residual...

Topics: High Energy Physics - Theory, High Energy Physics - Phenomenology

Source: http://arxiv.org/abs/1604.07696

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Jul 19, 2013
07/13

by
Philip D. Mannheim

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We propose that gravity be intrinsically quantum-mechanical, so that in the absence of quantum mechanics the geometry of the universe would be Minkowski. We show that in such a situation gravity does not require any independent quantization of its own, with it being quantized simply by virtue of its being coupled to the quantized matter fields that serve as its source. We show that when the gravitational and matter fields possess an underlying conformal symmetry, the gravitational field and...

Source: http://arxiv.org/abs/1005.5108v4

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Sep 21, 2013
09/13

by
Philip D. Mannheim; James G. O'Brien

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We apply the conformal gravity theory to a sample of 111 spiral galaxies whose rotation curve data points extend well beyond the optical disk. With no free parameters other than galactic mass to light ratios, the theory is able to account for the systematics that is observed in this entire set of rotation curves without the need for any dark matter at all. In previous applications of the theory a central role was played by a universal linear potential term $V(r)=\gamma_0 c^2r/2$ that is...

Source: http://arxiv.org/abs/1011.3495v4

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Jul 20, 2013
07/13

by
Philip D. Mannheim

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We identify an apparent imprint of the global Hubble flow on the systematics of galactic rotation curves, and discuss its possible implications for gravitational theory.

Source: http://arxiv.org/abs/astro-ph/9712090v1

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Jun 30, 2018
06/18

by
Philip D. Mannheim

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Even though Faraday's Law is a dynamical law that describes how changing $\bf{E}$ and $\bf {B}$ fields influence each other, by introducing a vector potential $A_{\mu}$ according to $F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}$ Faraday's Law is satisfied kinematically, with the relation $(-g)^{-1/2}\epsilon^{\mu\nu\sigma\tau}\nabla_{\nu}F_{\sigma\tau}=0$ holding on every path in a variational procedure or path integral. In a space with torsion $Q_{\alpha\beta\gamma}$ the axial vector...

Topics: High Energy Physics - Theory, General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1406.2265

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3.0

Jun 30, 2018
06/18

by
Philip D. Mannheim

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We present some interesting connections between $PT$ symmetry and conformal symmetry. We use them to develop a metricated theory of electromagnetism in which the electromagnetic field is present in the geometric connection. However, unlike Weyl who first advanced this possibility, we do not take the connection to be real but to instead be $PT$ symmetric, with it being $iA_{\mu}$ rather than $A_{\mu}$ itself that then appears in the connection. With this modification the standard minimal...

Topics: High Energy Physics - Theory, General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1407.1820

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Sep 18, 2013
09/13

by
Philip D. Mannheim

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We trace the origin of the cosmological constant problem to the assumption that Newton's constant $G$ sets the scale for cosmology. And then we show that once this assumption is relaxed, the very same cosmic acceleration which has served to make the cosmological constant problem so very severe instead then serves to provide us with its potential resolution. We present an alternate cosmology, one based on conformal gravity, and show that once given only that the sign of the vacuum energy density...

Source: http://arxiv.org/abs/gr-qc/9903005v2

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Sep 18, 2013
09/13

by
Philip D. Mannheim

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With attempts to quench the cosmological constant $\Lambda$ having so far failed, we instead investigate what could be done if $\Lambda$ is not quenched and actually gets to be as big as elementary particle physics suggests. Since the quantity relevant to cosmology is actually $\Omega_{\Lambda}$, quenching it to its small measured value is equally achievable by quenching not $\Lambda$ but $G$ instead, with the $G$ relevant to cosmology then being much smaller than that measured in a low energy...

Source: http://arxiv.org/abs/astro-ph/9901219v2

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Sep 19, 2013
09/13

by
Philip D. Mannheim

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We show that detailed exploration of the $11$ region, one is thus currently unable to ascertain whether the universe is accelerating or decelerating between $z=1$ and $z=2$. To be able to visualize the supernovae and radio galaxy data simultaneously, we present a representation of the radio galaxy data in terms of an equivalent apparent magnitude Hubble diagram. We discuss briefly some implications of the anisotropies in the cosmic microwave background for the conformal theory, and show that in...

Source: http://arxiv.org/abs/astro-ph/0302362v1

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Sep 20, 2013
09/13

by
Philip D. Mannheim; Ionel Simbotin

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We establish the completeness of some characteristic sets of non-normalizable modes by constructing fully localized square steps out of them, with each such construction expressly displaying the Gibbs phenomenon associated with trying to use a complete basis of modes to fit functions with discontinuous edges. As well as being of interest in and of itself, our study is also of interest to the recently introduced large extra dimension brane-localized gravity program of Randall and Sundrum, since...

Source: http://arxiv.org/abs/hep-th/0607090v1

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Sep 20, 2013
09/13

by
Philip D. Mannheim

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We present a solution to the ghost problem in fourth order derivative theories. In particular we study the Pais-Uhlenbeck fourth order oscillator model, a model which serves as a prototype for theories which are based on second plus fourth order derivative actions. Via a Dirac constraint method quantization we construct the appropriate quantum-mechanical Hamiltonian and Hilbert space for the system. We find that while the second-quantized Fock space of the general Pais-Uhlenbeck model does...

Source: http://arxiv.org/abs/hep-th/0608154v2

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Sep 18, 2013
09/13

by
Philip D. Mannheim; James G. O'Brien

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We review some recent work by Mannheim and O'Brien on the systematics of galactic rotation curves in the conformal gravity theory. In this work the conformal theory was applied to a comprehensive, high quality sample of spiral galaxies whose rotation curves extend well beyond the galactic optical disks. On galactic scales the conformal gravitational theory departs from the standard Newtonian theory in two distinct ways. One is a local way in which local matter sources within galaxies generate...

Source: http://arxiv.org/abs/1211.0188v1

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Jul 20, 2013
07/13

by
Carl M. Bender; Philip D. Mannheim

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In nonrelativistic quantum mechanics and in relativistic quantum field theory, time t is a parameter and thus the time-reversal operator T does not actually reverse the sign of t. However, in relativistic quantum mechanics the time coordinate t and the space coordinates x are treated on an equal footing and all are operators. In this paper it is shown how to extend PT symmetry from nonrelativistic to relativistic quantum mechanics by implementing time reversal as an operation that changes the...

Source: http://arxiv.org/abs/1107.0501v1

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Sep 22, 2013
09/13

by
Philip D. Mannheim; Aharon Davidson

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Using the Dirac constraint method we show that the pure fourth-order Pais-Uhlenbeck oscillator model is free of observable negative norm states. Even though such ghosts do appear when the fourth order theory is coupled to a second order one, the limit in which the second order action is switched off is found to be a highly singular one in which these states move off shell. Given this result, construction of a fully unitary, renormalizable, gravitational theory based on a purely fourth order...

Source: http://arxiv.org/abs/hep-th/0001115v1

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Sep 18, 2013
09/13

by
Philip D. Mannheim

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In this paper we identify a new regularity in the systematics of galactic rotation curves, namely we find that at the last detected points in galaxies of widely varying luminosity, the centripetal acceleration is found to have the completely universal form $v^2/R=c^2(\gamma_0+\gamma^{*}N^{*})/2$ where $\gamma_0$ and $\gamma^{*}$ are new universal constants and $N^{*}$ is the amount of visible matter in each galaxy. This regularity points to a role for the linear potentials associated with...

Source: http://arxiv.org/abs/astro-ph/9605085v1

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Sep 21, 2013
09/13

by
Philip D. Mannheim

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We make a first application of the linear gravitational potentials of the conformal gravity theory to the distance scale associated with clusters of galaxies, with the theory being found to give a reasonable value for the mean velocity of the virialized core of the typical Coma cluster, with no need to invoke the existence of dark matter.

Source: http://arxiv.org/abs/astro-ph/9508045v1

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Sep 21, 2013
09/13

by
Philip D. Mannheim

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Possibly the most peculiar expectation of the standard fine-tuned cosmological paradigm is that cosmic acceleration is to only be a very recent (z

Source: http://arxiv.org/abs/astro-ph/0104022v2

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Sep 18, 2013
09/13

by
Philip D. Mannheim

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We discuss some implications of the current round of galactic dark matter searches for galactic rotation curve systematics and dynamics, and show that these new data do not invalidate the conformal gravity program of Mannheim and Kazanas which has been advanced as a candidate alternative to both the standard second order Newton-Einstein theory and the need for dark matter.

Source: http://arxiv.org/abs/astro-ph/9412007v1

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Sep 20, 2013
09/13

by
Philip D. Mannheim

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Our long experience with Newtonian potentials has inured us to the view that gravity only produces local effects. In this paper we challenge this quite deeply ingrained notion and explicitly identify some intrinsically global gravitational effects. In particular we show that the global cosmological Hubble flow can actually modify the motions of stars and gas within individual galaxies, and even do so in a way which can apparently eliminate the need for galactic dark matter. Also we show that a...

Source: http://arxiv.org/abs/gr-qc/9611038v1

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Jul 22, 2013
07/13

by
Carl M. Bender; Philip D. Mannheim

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The Pais-Uhlenbeck model is a quantum theory described by a higher-derivative field equation. It has been believed for many years that this model possesses ghost states (quantum states of negative norm) and therefore that this model is a physically unacceptable quantum theory. The existence of such ghost states was believed to be attributable to the field equation having more than two derivatives. This paper shows that the Pais-Uhlenbeck model does not possess any ghost states at all and that...

Source: http://arxiv.org/abs/0807.2607v1

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Sep 22, 2013
09/13

by
Philip D. Mannheim

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We discuss the circumstances under which gravity might be repulsive rather than attractive. In particular we show why our standard solar system distance scale gravitational intuition need not be a reliable guide to the behavior of gravitational phenomena on altogether larger distance scales such as cosmological, and argue that in fact gravity actually gets to act repulsively on such distance scales. With such repulsion a variety of current cosmological problems (the flatness, horizon, dark...

Source: http://arxiv.org/abs/gr-qc/0001011v1

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Sep 22, 2013
09/13

by
Philip D. Mannheim

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We discuss some outstanding open questions regarding the validity and uniqueness of the standard second order Newton-Einstein classical gravitational theory. On the observational side we discuss the degree to which the realm of validity of Newton's Law of Gravity can actually be extended to distances much larger than the solar system distance scales on which the law was originally established. On the theoretical side we identify some commonly accepted but actually still open to question...

Source: http://arxiv.org/abs/gr-qc/9306025v1

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Jul 20, 2013
07/13

by
Philip D. Mannheim

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We show that the embedding of either a static or a time dependent maximally 3-symmetric brane with non-zero spatial curvature $k$ into a non-compactified $AdS_5$ bulk does not yield exponential suppression of the geometry away from the brane. Implications of this result for brane-localized gravity are discussed.

Source: http://arxiv.org/abs/hep-th/0009065v2

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Jul 20, 2013
07/13

by
Philip D. Mannheim

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We review the current status and prospects for the conformal invariant fourth order theory of gravity which has recently been advanced by Mannheim and Kazanas as a candidate alternative to the standard second order Einstein theory. We examine how it is possible in principle to replace the Einstein theory at all while retaining its tested features, and we appeal to the wisdom gleaned from particle physics to suggest a fully covariant, conformal invariant alternative. We explore the theory as a...

Source: http://arxiv.org/abs/gr-qc/9407010v1

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Jul 20, 2013
07/13

by
Carl M. Bender; Philip D. Mannheim

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In a recent paper Bender and Mannheim showed that the unequal-frequency fourth-order derivative Pais-Uhlenbeck oscillator model has a realization in which the energy eigenvalues are real and bounded below, the Hilbert-space inner product is positive definite, and time evolution is unitary. Central to that analysis was the recognition that the Hamiltonian $H_{\rm PU}$ of the model is PT symmetric. This Hamiltonian was mapped to a conventional Dirac-Hermitian Hamiltonian via a similarity...

Source: http://arxiv.org/abs/0804.4190v1

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Jun 27, 2018
06/18

by
Philip D. Mannheim

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Recently in Phys. Rev. D 88, 027504 (2013) Yoon has suggested that there may be problems for the non-relativistic limit of the conformal gravity theory. Here we show that Yoon's results only hold because of the assumption that gravitational sources can be treated the same way that they are treated in standard Newton-Einstein gravity. Since such an assumption violates the theory's underlying conformal invariance,Yoon's conclusions are invalidated.

Topics: General Relativity and Quantum Cosmology, High Energy Physics - Theory

Source: http://arxiv.org/abs/1506.02479

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Sep 20, 2013
09/13

by
Philip D. Mannheim

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For the Randall-Sundrum brane world where a positive tension Minkowski brane is embedded in AdS5, two candidate propagators have been suggested in the literature, one being based on the normalized mode solutions to the source-free volcano potential fluctuation equation, and the other being the Giddings, Katz and Randall outgoing Hankel function based one. We show that while both of these two propagators have the same pole plus cut singularity structure in the complex energy plane, they behave...

Source: http://arxiv.org/abs/hep-th/0607041v1

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Sep 19, 2013
09/13

by
Philip D. Mannheim

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We present a solution to the cosmological constant, the zero-point energy, and the quantum gravity problems within a single comprehensive framework. We show that in quantum theories of gravity in which the zero-point energy density of the gravitational field is well-defined, the cosmological constant and zero-point energy problems solve each other by mutual cancellation between the cosmological constant and the matter and gravitational field zero-point energy densities. Because of this...

Source: http://arxiv.org/abs/0909.0212v5

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Jun 28, 2018
06/18

by
Philip D. Mannheim

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While a Hamiltonian can be both Hermitian and $PT$ symmetric, it is $PT$ symmetry that is the more general, as it can lead to real energy eigenvalues even if the Hamiltonian is not Hermitian. We discuss some specific ways in which $PT$ symmetry goes beyond Hermiticity and is more far reaching than it. We show that simply by virtue of being the generator of time translations, the Hamiltonian must always be $PT$ symmetric, regardless of whether or not it might be Hermitian. We show that the...

Topics: Quantum Physics, High Energy Physics - Phenomenology

Source: http://arxiv.org/abs/1506.08432

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Sep 19, 2013
09/13

by
Philip D. Mannheim

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In this paper we present a general, model independent analysis of a recently detected apparent cosmic repulsion, and discuss its potential implications for gravitational theory. In particular, we show that a negatively spatially curved universe acts like a diverging refractive medium, to thus naturally cause galaxies to accelerate away from each other. Additionally, we show that it is possible for a cosmic acceleration to only be temporary, with some accelerating universes actually being able...

Source: http://arxiv.org/abs/astro-ph/9804335v1

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Sep 20, 2013
09/13

by
Philip D. Mannheim

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In this review we discuss the connection between two seemingly disparate topics, macroscopic gravity on astrophysical scales and Hamiltonians that are not Hermitian but $PT$ symmetric on microscopic ones. In particular we show that the quantum-mechanical unitarity problem of the fourth-order derivative conformal gravity theory is resolved by recognizing that the scalar product appropriate to the theory is not the Dirac norm associated with a Hermitian Hamiltonian but is instead the norm...

Source: http://arxiv.org/abs/1205.5717v1

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Sep 18, 2013
09/13

by
Philip D. Mannheim

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Some recent supernovae studies have extended the distance versus velocity Hubble plot to very high redshift, and have revealed the apparent presence of a cosmic repulsion. We show that such a repulsion has a natural origin within conformal gravity, a fully covariant candidate alternative to standard gravity, and that it arises from the gravitational field itself via the negative spatial curvature which conformal cosmology is required to possess. In this same cosmology the flatness, horizon and...

Source: http://arxiv.org/abs/astro-ph/9803135v1

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Sep 18, 2013
09/13

by
Michael Y. Hu; Wolfgang Sturhahn; Thomas S. Toellner; Philip D. Mannheim; Dennis E. Brown; Jiyong Zhao; E. Ercan Alp

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Nuclear resonant inelastic x-ray scattering is used to measure the projected partial phonon density of states of materials. A relationship is derived between the low-energy part of this frequency distribution function and the sound velocity of materials. Our derivation is valid for harmonic solids with Debye-like low-frequency dynamics. This method of sound velocity determination is applied to elemental, composite, and impurity samples which are representative of a wide variety of both...

Source: http://arxiv.org/abs/cond-mat/0212387v2

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Sep 18, 2013
09/13

by
Philip D. Mannheim

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We show that within the cosmology associated with conformal gravity the age of the universe is given as $1/H_0$, to thus overcome the current cosmological age crisis. We show that while the parameter $\Omega_{mat} = \rho_{mat} / \rho_C$ takes on all values between zero and infinity in conformal gravity, nonetheless it is of order one (but not identically equal to one) for half a Hubble time to thus naturally explain its current closeness to one without fine tuning. We show that the cosmological...

Source: http://arxiv.org/abs/astro-ph/9601071v1

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Sep 19, 2013
09/13

by
Philip D. Mannheim

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We present a simple, closed form expression for the potential of an axisymmetric disk of stars interacting through gravitational potentials of the form $V(r)=-\beta /r+\gamma r/2$, the potential associated with fundamental sources in the conformal invariant fourth order theory of gravity which has recently been advanced by Mannheim and Kazanas as a candidate alternative to the standard second order Einstein theory. Using the model we obtain a reasonable fit to some representative galactic...

Source: http://arxiv.org/abs/astro-ph/9307003v1

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Sep 23, 2013
09/13

by
Philip D. Mannheim; James G. O'Brien; David Eric Cox

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We show that the standard perfect fluid paradigm is not necessarily a valid description of a curved space steady state gravitational source. Simply by virtue of not being flat, curved space geometries have to possess intrinsic length scales, and such length scales can affect the fluid structure. For modes of wavelength of order or greater than such scales eikonalized geometrical optics cannot apply and rays are not geodesic. Covariantizing thus entails not only the replacing of flat space...

Source: http://arxiv.org/abs/0903.4381v2

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Sep 18, 2013
09/13

by
Philip D. Mannheim

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We outline a program with the potential to solve both the cosmological constant and quantum gravity problems within a single, comprehensive framework, one that is formulated entirely in four spacetime dimensions. The program is based on an interplay between the dynamical symmetry breaking of particle physics and a gravity theory, conformal gravity, which possesses an underlying local conformal invariant structure. Central to the discussion is the recognition that when symmetry is broken...

Source: http://arxiv.org/abs/0809.1200v2

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59

Sep 19, 2013
09/13

by
Philip D. Mannheim

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In the first paper in this series we presented a typical set of galactic rotation curves associated with the conformal invariant fourth order theory of gravity which has recently been advanced by Mannheim and Kazanas as a candidate alternative to the standard second order Einstein theory. Reasonable agreement with data was obtained for four representative galaxies without the need for any non-luminous or dark matter. In this second paper we present the associated formalism. Additionally, we...

Source: http://arxiv.org/abs/astro-ph/9307004v1